Q3-Q2 will be greater than the distance of Q2-Q1 in a distribution of scores that is
A) normal.
B) positively skewed.
C) negatively skewed.
D) symmetrical.

Question

Quizplus · Accepted Answer

In a positively skewed distribution, the majority of the scores are on the lower end of the distribution, pulling the median down towards the lower end and creating a long tail of higher scores. Therefore, the distance between Q3 (the upper quartile) and Q2 (the median) will be larger than the distance between Q2 and Q1 (the lower quartile). In contrast, a symmetrical distribution (Option D) would have equal distances between quartiles, while a negatively skewed distribution (Option C) would have a longer tail of lower scores and a smaller distance between Q3 and Q2, compared to Q2 and Q1. A normal distribution (Option A) is symmetrical and therefore would not have a difference between the distances of Q3-Q2 and Q2-Q1.

Q3-Q2 Will Be Greater Than the Distance of Q2-Q1 in a Distribution